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Thomsen's theorem, named after Gerhard Thomsen, is a theorem in elementary geometry. It shows that a certain path constructed by line segments being parallel to the edges of a triangle always ends up at its starting point.
Thomsen wrote 22 papers on various topics in geometry and furthermore a few papers on theoretical physics as well. The latter were mostly written in Italian rather than in German. Thomsen also wrote a book on the foundations of elementary geometry. [1] In elementary geometry Thomsen's theorem is named after him. [5]
geodesic sphere {3,5+} 3,3: 282 37147.294418462 0 0 0 12 270 0 0 840 560 0 12.166° geodesic sphere {3,5+} 4,2: 292 39877.008012909 0 0 0 12 280 0 0 870 580 0 11.857° 306 43862.569780797 0 0 0 12 294 0 0 912 608 0 11.628° 312 45629.313804002 0.000306163 0 0 12 300 0 0
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Set square shaped as 45° - 45° - 90° triangle The side lengths of a 45° - 45° - 90° triangle 45° - 45° - 90° right triangle of hypotenuse length 1.. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right angle (90°, π / 2 radians) and two other congruent angles each measuring half of a right angle (45°, or ...
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.